Abstract

A method for restoring an optical image which is subjected to low-pass frequency filtering is presented. It is assumed that the object whose image is restored is of finite spatial extent. The problem is treated as an algebraic image-restoration problem which is then solved as a quadratic programming problem with bounded variables. The regularization technique for the ill-posed system is to replace the consistent system of the quadratic programming problem by an approximate system of smaller rank. The rank which gives a best or near-best solution is estimated. This method is a novel one, and it compares favorably with other known methods. Computer-simulated examples are presented. Comments and conclusions are given.

© 1983 Optical Society of America

Restoration of images with missing high-frequency components by minimizing the L₁ norm of the solution vector

Nabih N. Abdelmalek and Nobuyuki Otsu
Appl. Opt. 24(10) 1415-1420 (1985)

Digital image restoration using quadratic programming

N. N. Abdelmalek and T. Kasvand
Appl. Opt. 19(19) 3407-3415 (1980)

Speed comparison among methods for restoring signals with missing high-frequency components using two different low-pass-filter matrix dimensions

Nabih N. Abdelmalek and Nobuyuko Otsu
Opt. Lett. 10(8) 372-374 (1985)

Image restoration for space invariant pointspread functions

N. N. Abdelmalek, T. Kasvand, and J. P. Croteau
Appl. Opt. 19(7) 1184-1189 (1980)

Direct algorithm for digital image restoration

N. N. Abdelmalek, T. Kasvand, J. Olmstead, and M. M. Tremblay
Appl. Opt. 20(24) 4227-4233 (1981)